Finally, we can also use the SCHA formalism to determine the magnetic susceptibility, which provides a valuable link
between theory and experimental measurements [1]}. Indeed, measurements from ISHE voltage in the NM side side
directly correspond with the real and imaginary part of the magnetic susceptibility, and they are commonly used
to get information about ferromagnetic damping. To obtain the susceptibility, we introduce the circularly polarized
magnetization
\(M_q^+=M_q^y+iM_q^z\approx \frac{g\mu _B}{a^3}\sqrt{2\tilde{S}}\rho _\textrm {eff}^{1/4}|\alpha _q|e^{-i(\Omega t-\phi _0)},\) 
